1. Field of the Invention
The present invention relates to the recovery of objects of any dimension using global models with parametric offsets. This recovery formulation allows for the creation of scalable default models which help to constrain the model fit in expected ways as well as aid in the assignment of model-data correspondences.
2. Description of the Prior Art
Different forms of hybrid models have been described in vision literature over the past several years. The following will focus only on those models most closely related to the present invention. In the models related to the present invention, the global component has been described by a parametric model or as a series of vibrational modes. Parametric models are described by D. Terzopoulos and D. Metaxas in "Dynamic 3D Models With Local And Global Deformations: Deformable Superquadrics", IEEE PAMI, 13(7):703-714, 1991; by J. Park, D. Metaxas and L. Axel in "Volumetric Deformable Models With Parametric Functions: A New Approach To The 3D Motion Analysis Of The LV From MRI-SPAMM", Proceedings of the 5th IEEE ICCV, MIT, Mass., pages 700-705, 1995; and by J. Park, D. Metaxas and A. Young in "Deformable Models With Parameter Functions: Application To Heart Wall Modeling", Proceedings of the IEEE CVPR, Seattle, Wash., pages 437-442, 1994. Vibrational modes are described by A. Pentland in "The Thingworld Modeling System: Virtual Sculpting By Modal Forces", Proceedings of SIGGRAPH, pages 143-144, 1990; and by B. C. Vemuri and A. Radisavljevic in "From Global To Local, A Continuum Of Shape Models With Fractal Priors", IEEE CVPR, pages 307-313, 1993.
A. Pentland and J. Williams in "Good Vibrations: Modal Dynamics For Graphics And Animation", Computer Graphics, 23(3):215-222, July 1989, presented the first use of hybrid modeling in the programming environment, ThingWorld. The system coupled a global geometric modal representation with a local description of the object's dynamics.
Terzopoulos and Metaxas included a global superquadric component in their deformable model. The deformations from this base superquadric model take the form of a thin membrane spline described using the Finite Element Method (FEM). Unlike Pentland's model, the underlying superquadric as well as the spline mesh deformed to fit the data.
Park, Metaxas and Young developed a thick ellipsoidal model for recovering 3-D cardiac motion from tagged-MR data. Their model, developed independently and in parallel with T. O'Donnell, A. Gupta and T. Boult in "The Hybrid Volumetric Ventriculoid: A Model For MR-SPAMM 3-D Analysis", Proceedings of Computers in Cardiology, IEEE, 1995, provided a piecewise plot of the change in relevant global LV characteristics. Their model, however, does not report strain and is recovered under the unrealistic assumption that the tag columns remain straight over the cardiac cycle. Their model formulation differs from the model formulation of the present invention in the following ways. First, their model does not have distinct global and local components. They use linear piecewise parametric functions to express local deformations. Second, the default shape of the model is a thick ellipsoid rather than a shape closer to a real LV. Third, their model does not provide a concise description of the LV movement. Rather, piecewise plots describe the motion. Fourth, their model assumes a dense tag acquisition and therefore makes no use of "regularizing" constraints.
As compared to the HVV, there is a clear distinction between global and offset components in this model, it differs from the approach of the present invention in that the offsets are not parametric.